# Components of an Electric field due to a dipole

1. Feb 16, 2010

### forensics409

1. The problem statement, all variables and given/known data
The problem is: Show that the components of $$\vec{E}$$ due to a dipole are given at distant points, by Ex=$$\frac{1}{4\pi\epsilon{o}}$$ $$\frac{3pxz}{(x^2+z^2)^{5/2}}$$ and Ez=$$\frac{1}{4\pi\epsilon{o}}$$ $$\frac{p(2z^2-x^2)}{(x^2+z^2)^(\frac{5}{2})}}$$

http://physweb.bgu.ac.il/COURSES/PHYSICS2_B/2009A/homework/Homework-2_files/image006.jpg [Broken]

2. Relevant equations

E=$$\frac{1}{4\pi\epsilon{o}}$$ $$\frac{Q}{r^2}$$
p=qd

3. The attempt at a solution

I have tried to break the fields of each one into vector components and add the components, however, it got really messy really quickly and after simplifying it a bit i got a ridiculous equation for just the x component, i had no clue where to go and gave up on even try to get the z component.

Ex=$$\frac{q}{4\pi\epsilon{o}}$$ $$\frac{(x^2+(z+\frac{d}{2})^{2})^{\frac{3}{2}}-(x^2+(z-\frac{d}{2})^{2})^{\frac{3}{2}}}{((x^{2}+z^{2})^{2} + (\frac{d^{2}x^{2}}{2}-\frac{d^{2}z^{2}}{2}+\frac{d^4}{16}))^{\frac{3}{2}}}$$

Last edited by a moderator: May 4, 2017